14 citations · 29 across the 19 of their papers we have counts for
24 papers
Propagation of anisotropic Gabor wave front sets
Patrik Wahlberg
We show a result on propagation of the anisotropic Gabor wave front set for linear operators with a tempered distribution Schwartz kernel. The anisotropic Gabor wave front set is p…
Propagation of anisotropic Gelfand-Shilov wave front sets
Patrik Wahlberg
We show a result on propagation of the anisotropic Gelfand--Shilov wave front set for linear operators with Schwartz kernel which is a Gelfand--Shilov ultradistribution of Beurling…
Anisotropic global microlocal analysis for tempered distributions
Luigi Rodino, Patrik Wahlberg
We study an anisotropic version of the Shubin calculus of pseudodifferential operators on . Anisotropic symbols and Gabor wave front sets are defined in terms of decay…
Microlocal analysis for Gelfand--Shilov spaces
Luigi Rodino, Patrik Wahlberg
We introduce an anisotropic global wave front set of Gelfand--Shilov ultradistributions with different indices for regularity and decay at infinity. The concept is defined by the l…
Pseudo-differential operators with isotropic symbols, Wick and anti-Wick operators, and hypoellipticity
Nenad Teofanov, Joachim Toft, Patrik Wahlberg
We study the link between pseudo-differential operators and Wick operators via the Bargmann transform. We deduce a formula for the symbol of the Wick operator in terms of the short…
Semigroups for quadratic evolution equations acting on Shubin-Sobolev and Gelfand-Shilov spaces
Patrik Wahlberg
We consider the initial value Cauchy problem for a class of evolution equations whose Hamiltonian is the Weyl quantization of a homogeneous quadratic form with non-negative definit…
The Gabor wave front set of compactly supported distributions
Patrik Wahlberg
We show that the Gabor wave front set of a compactly supported distribution equals zero times the projection on the second variable of the classical wave front set.
Shubin type Fourier integral operators and evolution equations
Marco Cappiello, René Schulz, Patrik Wahlberg
We study the Cauchy problem for an evolution equation of Schrödinger type. The Hamiltonian is the Weyl quantization of a real homogeneous quadratic form with a pseudodifferential p…
Lagrangian distributions and Fourier integral operators with quadratic phase functions and Shubin amplitudes
Marco Cappiello, René Schulz, Patrik Wahlberg
We study Fourier integral operators with Shubin amplitudes and quadratic phase functions associated to twisted graph Lagrangians with respect to symplectic matrices. We factorize s…
Conormal distributions in the Shubin calculus of pseudodifferential operators
Marco Cappiello, René Schulz, Patrik Wahlberg
We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of an FBI transform. Based on this we introduce as a generalization a new class of temp…
The Weyl product on quasi-Banach modulation spaces
Yuanyuan Chen, Joachim Toft, Patrik Wahlberg
We study the bilinear Weyl product acting on quasi-Banach modulation spaces. We find sufficient conditions for continuity of the Weyl product and we derive necessary conditions. Th…
Propagation of exponential phase space singularities for Schrödinger equations with quadratic Hamiltonians
Evanthia Carypis, Patrik Wahlberg
We study propagation of phase space singularities for the initial value Cauchy problem for a class of Schrödinger equations. The Hamiltonian is the Weyl quantization of a quadratic…
Microlocal properties of Shubin pseudodifferential and localization operators
René Schulz, Patrik Wahlberg
We investigate global microlocal properties of localization operators and Shubin pseudodifferential operators. The microlocal regularity is measured in terms of a scale of Shubin-t…
Propagation of polynomial phase space singularities for Schrödinger equations with quadratic Hamiltonians
Patrik Wahlberg
We study propagation of phase space singularities for a Schrödinger equation with a Hamiltonian that is the Weyl quantization of a quadratic form with non-negative real part. Phase…
Propagation of Gabor singularities for Schrödinger equations with quadratic Hamiltonians
Karel Pravda-Starov, Luigi Rodino, Patrik Wahlberg
We study propagation of the Gabor wave front set for a Schrödinger equation with a Hamiltonian that is the Weyl quantization of a quadratic form with non-negative real part. We poi…
Sharp results for the Weyl product on modulation spaces
Elena Cordero, Joachim Toft, Patrik Wahlberg
We give sufficient and necessary conditions on the Lebesgue exponents for the Weyl product to be bounded on modulation spaces. The sufficient conditions are obtained as the restric…
The equality of the homogeneous and the Gabor wave front set
René Schulz, Patrik Wahlberg
We prove that Hörmander's global wave front set and Nakamura's homogeneous wave front set of a tempered distribution coincide. In addition we construct a tempered distribution with…
The Gabor wave front set
Luigi Rodino, Patrik Wahlberg
We define the Gabor wave front set of a tempered distribution in terms of rapid decay of its Gabor coefficients in a conic subset of the phase space. We show the incl…
Schrödinger type propagators, pseudodifferential operators and modulation spaces
Elena Cordero, Anita Tabacco, Patrik Wahlberg
We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of nondegenera…
Embeddings of -modulation spaces
Joachim Toft, Patrik Wahlberg
We show upper and lower embeddings of -modulation spaces in -modulation spaces for , and prove partial results on the sharpness of the embeddi…
Representations of almost periodic pseudodifferential operators and applications in spectral theory
Patrik Wahlberg
The paper concerns algebras of almost periodic pseudodifferential operators on with symbols in Hörmander classes. We study three representations of such algebras, one…
Almost periodic pseudodifferential operators and Gevrey classes
Alessandro Oliaro, Luigi Rodino, Patrik Wahlberg
We study almost periodic pseudodifferential operators acting on almost periodic functions $G_{\rm ap}^s(\rr d)$ of Gevrey regularity index . We prove that almost periodic…
On the instantaneous frequency of Gaussian stochastic processes
Patrik Wahlberg, Peter J. Schreier
This paper concerns the instantaneous frequency (IF) of continuous-time, zero-mean, complex-valued, proper, mean-square differentiable nonstationary Gaussian stochastic processes.…
The wave front set of the Wigner distribution and instantaneous frequency
Paolo Boggiatto, Alessandro Oliaro, Patrik Wahlberg
We prove a formula expressing the gradient of the phase function of a function as a normalized first frequency moment of the Wigner distribution…